Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
624 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×#1044 | C2 | semidirect |
| 3. C2×C4×#1043 | C2 | semidirect |
| 5. #11716776 | C2 | semidirect |
| 10. C2×C4×C5×D5 | C4 | semidirect |
| 12. C2×D5×Dic5 | C4 | semidirect |
| 17. #87831 | C4 | direct (N × H) |
| 27. C2×#1044 | C2×C4 | semidirect |
| 30. C2×#1043 | C2×C4 | semidirect |
| 53. C2×C5×D5 | C42 | semidirect |
| 58. C4×C52 | C22⋊C4 | semidirect |
| 59. #1039 | C22⋊C4 | semidirect |
| 73. C2×C4×D5 | AGL(1,𝔽5) | semidirect |
| 123. C52 | C4×C22⋊C4 | semidirect |
| 141. C2×D5 | C4×AGL(1,𝔽5) | semidirect |
| 147. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 197. C5 | C4×C22⋊AGL(1,𝔽5) | semidirect |
| 212. C4 | #87831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C2×C4×#1044 | 2 |
| C2×C4×#1043 | 2 |
| C2×#87831 | 2 |
| #11716776 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 5 |